“A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known.”

— Deane Montgomery

[Properties of finite-dimensional groups, Proceedings of the International Mathematical Congress held in Cambridge, Mass. in 1950, 442–446, University of Toronto Press, 1952, http://www.mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0442.0446.ocr.pdf] (quote from p. 442)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "A group which has a simple structure may offer difficult questions when operating as a transformation group. For exampl…" by Deane Montgomery?

Deane Montgomery 2

American mathematician 1909–1992

Harold Chestnut (1917–2001) American engineer

Source: Systems Engineering Tools, (1965), Systems Engineering Methods (1967), p. 70; Rest of first paragraph of Ch.3

“In 1946, a Macy Foundation interdisciplinary conference was organized to use the model provided by "feedback systems," honorifically referred to in earlier conferences as "teleological mechanisms," and later as "cybernetics," with the expectation that this model would provide a group of sciences with useful mathematical tools and, simultaneously, would serve as a form of cross-disciplinary communication. Out of the deliberations of this group came a whole series of fruitful developments of a very high order. Kurt Lewin (who died in 1947) took away from the first meeting the term "feedback". He suggested ways in which group processes, which he and his students were studying in a highly disciplined, rigorous way, could be improved by a "feedback process," as when, for example, a group was periodically given a report on the success or failure of its particular operations.”

Margaret Mead (1901–1978) American anthropologist

Source: 1960s, Continuities in Cultural Evolution (1964), p. 272-273

“The present report is a preliminary summary on one phase of a series of experimental studies of group life which has as its aim a scientific approach to such questions as the following : What underlies such differing patterns of group behavior as rebellion against authority, persecution of a scapegoat, apathetic submissiveness to authoritarian domination, or attack upon an outgroup? How may differences in subgroup structure, group stratification, and potency of ego- centered and group-centered goals be utilized as criteria for predicting the social resultants of different group atmospheres? Is not democratic group life more pleasant, but authoritarianism more efficient?”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, Patterns of aggressive behavior in experimentally created “social climates”, 1939, p. 271.

“The group self or "we" is simply an "I" which includes other persons. One identifies himself with a group and speaks of the common will, opinion, service, or the like in terms of "we" and "us." The sense of it is stimulated by co-operation within and opposition without.”

Charles Cooley (1864–1929) American sociologist

Source: Human Nature and the Social Order, 1902, p. 209

“Whilst the distinction of ‘society’ and ‘individual’ has colloquial (and political) meaning, those inclined to the analysis of complex systems are more likely to ask which groups or societies are real individuals, exhibiting functional or behavioral integrity, as self-reproducing wholes. In pursuing this line of investigation, it is far more relevant to discriminate between types of groups than between groups and individuals, or even wholes and parts. It is especially helpful to distinguish feature groups from unit groups.”

Nick Land (1962) British philosopher

"Kinds of Killing" https://web.archive.org/web/20121111032625/http://www.thatsmags.com/shanghai/article/1008/kinds-of-killing (2011) (original emphasis)

“Whether it is committed by a group operating within or without the law, terrorism is still terrorism.”

Ilana Mercer South African writer

“In Defense of Obama’s Apologizing,” http://www.ilanamercer.com/phprunner/public_article_list_view.php?editid1=551 WorldNetDaily.com, May 21, 2010.
2010s, 2010

“They operate by administrative discretion and authority, not the rule of law: There is no legislature, no group lawmaking body.”

Charles A. Reich (1928–2019) American lawyer

The Liberals' Mistake (1987)
Context: Liberals placed an unreasonable amount of faith in large institutions: unions, foundations, big government, large corporations, and universities. These institutions are based on principles that are antithetical to democracy. They are not democratic, they are hierarchical: Someone is at the top and everybody else is at the bottom. Their policies are not made democratically, they are made at the top. These institutions are also not egalitarian. They operate by administrative discretion and authority, not the rule of law: There is no legislature, no group lawmaking body.
The individual in the large organization does not have the kind of constitutional rights that an individual in the society at large has. There are no protections of autonomy and free speech. Employees can be fired for many reasons. We need to constitutionalize large organizations to protect the people within them, to ensure that they can be politically outspoken.

“Early this Wednesday morning, at around 3 am, a security operation carried out by special forces that included security and military personnel, ended and was successful in achieving its goals. Seven members of the outlaw group were killed, this group are misguided and misleading, they are a terrorist group connected to terrorist organizations, and had planned to disrupt the security of the country and its people.”

Abdullah Ensour (1939) prime minister of Jordan

Jordanian Intelligence forces uncovered and stopped a Daesh plot to target civilians and military in Amman on March 1, 2016, Ensour addressed the parliament on March 2, 2016 on the successful attack on Daesh militants, quoted on Albawaba, "Jordanian authorities confirm Daesh activity in Irbid, suicide belts found" http://www.albawaba.com/news/jordanian-authorities-confirm-daesh-activity-irbid-suicide-belts-found-812292, March 2, 2016.

“Let me give you another, the way in which group membership can entrain language-usages that are self-deceptive. You can divide people into in-groups or out-groups, or use naturally occurring in-groups and out-groups, and if someone's a member of your in-group and they do something nice, you give a general description of it – "he's a generous person".”

Robert Trivers (1943) American evolutionary biologist and sociobiologist

As quoted in Science at the Edge: Conversations with the Leading Scientific Thinkers of Today (2008), p. 170
Context: People are often unconscious of some of the mechanisms that naturally occur in them in a biased way. For example, if I do something that is beneficial to you or to others, I will use the active voice: I did this, I did that, then benefits rained down on you. But if I did something that harmed others, I unconsciously switch to a passive voice: this happened, then that happened, then unfortunately you suffered these costs. One example I always loved was a man in San Francisco who ran into a telephone pole with his car, and he described it to the police as, "the pole was approaching my car, I attempted to swerve out-of-the-way, when it struck me."
Let me give you another, the way in which group membership can entrain language-usages that are self-deceptive. You can divide people into in-groups or out-groups, or use naturally occurring in-groups and out-groups, and if someone's a member of your in-group and they do something nice, you give a general description of it – "he's a generous person". If they do something negative, you state a particular fact: "in this case he misled me", or something like that. But it's exactly the other way around for an out-group member. If an out-group member does something nice, you give a specific description of it: "she gave me directions to where I wanted to go". But if she does something negative, you say, "she's a selfish person". So these kinds of manipulations of reality are occurring largely unconsciously.

“The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe - provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three· dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum entropy priors”

Roger Shepard (1929) American psychologist

R. N. Shepard, (1994). "Perceptual-cognitive universals as reflections of the world." Psychonomic Bulletin and Review, 1, 2–28.

“A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known.”

Help us to complete the source, original and additional information

Deane Montgomery 2

Related quotes

Related topics